Question

Prove that log a, log ar, log ar^2 is an a.p.

Is the following below correct?
Log ar^2 - Log ar= Log ar - Log a

hence applying laws of logarithm
Log(ar^2/ar) = log(ar/a)

Log and log cancels out and then cross-multiply
hence a^2r^2 = a^2r^2
L.H.S=R.H.S

Hence proved?

Answer 1

log a, log ar, log ar2, ...log a (r)^n

now, log ar^n=log a + n log r
consider the next term
log ar^(n+1)= log a + (n+1)log r

then

log ar^(n+1)-log ar^n= log r which is a constant. Therefor, the progression is arithemetic.